Estimate Population Using Random Samples Worksheets [PDF] (7.SP.A ... - Free Printable

This worksheet is about using random samples to estimate characteristics of a larger population. The key idea is that if you have a random sample, the proportion (or percentage) of people in the sample with a certain trait should be approximately the same as the proportion in the entire population.

We use the formula:

> Estimated Population Total = (Number in Sample with Trait / Sample Size) × Total Population

But since we’re trying to find the Total Population, and we know the Number in Population with Trait, we rearrange it:

> Total Population ≈ (Number in Population with Trait × Sample Size) / Number in Sample with Trait

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Let’s solve each problem step by step.

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Problem 1

> There are 75 students at the Olympiad whose favorite subject is Math. In a random survey of 636 students participating in the event, it was found that 53 students selected Math as their favorite subject. What is the best estimate for the total number of students participating in the event?

- We know:
- Number in population who like Math = 75
- Sample size = 636
- Number in sample who like Math = 53

We assume the sample proportion reflects the population proportion.

So,

> Total Students ≈ (75 × 636) / 53

Let’s compute:

First, 75 × 636 = 47,700

Then, 47,700 ÷ 53 = ?

Divide:
53 × 900 = 47,700 → Exactly!

✔ Answer: 900

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Problem 2

> At McCbride Middle School 65 students chose basketball as their preferred sport to play. If a survey of 672 random students at the school found that 56 students preferred to play basketball, what is the best estimate for the total number of students at McCbride Middle School?

- Known:
- Population who like basketball = 65
- Sample size = 672
- Sample who like basketball = 56

> Total Students ≈ (65 × 672) / 56

Compute:

First, 65 × 672

Break it down:
65 × 600 = 39,000
65 × 72 = 4,680
→ Total = 39,000 + 4,680 = 43,680

Now divide by 56:

43,680 ÷ 56

Try dividing:
56 × 780 = 56 × 700 = 39,200; 56 × 80 = 4,480 → 39,200 + 4,480 = 43,680

✔ Answer: 780

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Problem 3

> 46 students took a metro bus to a field trip at a museum. If a random survey of 364 random students at the field trip found that 28 students took the metro bus, what is the best estimate for the total number of students on the field trip?

- Known:
- Population who took metro = 46
- Sample size = 364
- Sample who took metro = 28

> Total Students ≈ (46 × 364) / 28

Compute:

First, 46 × 364

Break it down:
46 × 300 = 13,800
46 × 64 = 2,944
→ Total = 13,800 + 2,944 = 16,744

Now divide by 28:

16,744 ÷ 28

Do division:

28 × 598 = ?
28 × 600 = 16,800 → too big
28 × 590 = 28 × 500 = 14,000; 28 × 90 = 2,520 → 14,000 + 2,520 = 16,520
Subtract: 16,744 - 16,520 = 224
28 × 8 = 224 → so 590 + 8 = 598

✔ Answer: 598

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Problem 4

> In Harris County there are 45 people who own a bird. In a survey of 450 randomly selected people 10 own a bird. Based on the survey what is the best estimate of the total population of Harris County?

- Known:
- Population who own a bird = 45
- Sample size = 450
- Sample who own a bird = 10

> Total Population ≈ (45 × 450) / 10

Compute:

45 × 450 = 20,250

20,250 ÷ 10 = 2,025

✔ Answer: 2,025

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## ✔ Final Answers:

1. 900
2. 780
3. 598
4. 2,025

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## 📌 Key Concept Recap:

You’re using proportional reasoning based on a random sample to estimate a population total. The logic is:

> *The ratio of “people with trait” in the sample should match the ratio in the whole population.*

So:
(Sample with trait) / (Sample size) ≈ (Population with trait) / (Total population)

Rearranged:
Total population ≈ (Population with trait × Sample size) / (Sample with trait)

This is a foundational concept in statistics — estimating population parameters from sample data.

Let me know if you want to visualize this with diagrams or practice more!